We have a call option on 3 dices with strike 3. What's the fair value of the call when it pays the min value of the 3 dices?
E.g if we throw and have 426, the min is 2 here and so call is OTM (S < K)
216 permutations (6^3)
min(6) = 1/216 x (6-3) = 0.0139 EV
(666)
min(5) = 8/215 x (5-3) = 0.0744 EV
(555 556 565 566 655 656 665 666)
min(4) = ?
I'm getting lost in the permutation formula to calculate the number of outcomes where the min. comes 4. Can someone help me figure out how to find out the correct # of outcomes with value 4?